Does the interpretation of a dummy main effect change when including interaction terms?

Question

I would like to make my question clear with a short example with a regression equation.

Let's assume we would like to predict console prices (Y) while using the age of the consoles, the consoles model, as well as one color dummy as independent variables. Furthermore, the color variable is interacted with the age and the model variable. The blue color variable is one, if the console's color is blue, otherwise zero.

${\rm price}_i\ =\ \beta_0\ +\ \beta_1{\rm age}_i+ \beta_2{\rm model}_i+\beta_3{\rm blue}_i + \beta_4{\rm blue*\rm age}_i + \beta_5{\rm blue * \rm model}_i+\upsilon_i$

1. Question: Does the interpretation of $\beta_3$ change when including the interaction terms?

I would guess no and interpret $\beta_3$, regardless of the inclusion of interaction terms as follows: "Consoles which have the color blue have on average a β3 higher/lower price than consoles with different colors, keeping everything else constant"

2. Question is it allowed to include two interactions with the same dummy as done with β4 and β5?

3. If yes, is the interpretation of β4 different when also β5 is included compared to a regression without the interaction term of β5.